Benchmarking and Fair Pricing Applied to Two Market Models

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Benchmarking and Fair Pricing Applied to Two Market Models

Author Info

Hardy Hulley () (School of Finance and Economics, University of Technology, Sydney)
Shane Miller (School of Finance and Economics, University of Technology, Sydney)
Eckhard Platen () (School of Finance and Economics, University of Technology, Sydney)

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Abstract

This paper considers a market containing both continuous and discrete noise. Modest assumptions ensure the existence of a growth optimal portfolio. Non-negative self-financing trading strategies, when benchmarked by this portfolio, are local martingales under the real-world measure. This justifies the fair pricing approach, which expresses derivative prices in terms of real-world conditional expectations of benchmarked payoffs. Two models for benchmarked primary security accounts are presented, and fair pricing formulas for some common contingent claims are derived.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 155.

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Length: 37
Date of creation: 01 Mar 2005
Date of revision:
Handle: RePEc:uts:rpaper:155

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Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

This paper has been announced in the following NEP Reports:

NEP-ALL-2005-04-16 (All new papers)
NEP-FIN-2005-04-16 (Finance)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341. [Downloadable!] (restricted)
Ingersoll, Jonathan E, Jr, 2000. "Digital Contracts: Simple Tools for Pricing Complex Derivatives," Journal of Business, University of Chicago Press, vol. 73(1), pages 67-88, January. [Downloadable!] (restricted)
I. Bajeux-Besnainou, R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," European Journal of Finance, Taylor and Francis Journals, vol. 3(4), pages 291-309, December. [Downloadable!] (restricted)
Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July. [Downloadable!] (restricted)
Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
Other versions:
- E. Platen, . "A Minimal Financial Market Model," Sonderforschungsbereich 373 2000-91, Humboldt Universitaet Berlin.
Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Other versions:
- Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Blackwell Publishing, vol. 16(1), pages 131-151. [Downloadable!] (restricted)
Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Eckhard Platen, 2003. "An Alternative Interest Rate Term Structure Model," Research Paper Series 97, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Other versions:
- Eckhard Platen, 2005. "An Alternative Interest Rate Term Structure Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(06), pages 717-735. [Downloadable!] (restricted)
Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
Other versions:
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]
Shane Miller & Eckhard Platen, 2004. "Two-Factor Model for Low Interest Rate Regimes," Research Paper Series 130, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Other versions:
- Shane Miller & Eckhard Platen, 2004. "A Two-Factor Model for Low Interest Rate Regimes," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 107-133, March. [Downloadable!] (restricted)
Shane Miller & Eckhard Platen, 2008. "Analytic Pricing of Contingent Claims Under the Real-World Measure," Research Paper Series 216, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Other versions:
- Shane M. Miller & Eckhard Platen, 2008. "Analytic Pricing Of Contingent Claims Under The Real-World Measure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 841-867. [Downloadable!] (restricted)
Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, March. [Downloadable!] (restricted)

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Shane Miller & Eckhard Platen, 2008. "Analytic Pricing of Contingent Claims Under the Real-World Measure," Research Paper Series 216, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Other versions:
- Shane M. Miller & Eckhard Platen, 2008. "Analytic Pricing Of Contingent Claims Under The Real-World Measure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 841-867. [Downloadable!] (restricted)
David Heath & Eckhard Platen, 2006. "Local volatility function models under a benchmark approach," Quantitative Finance, Taylor and Francis Journals, vol. 6(3), pages 197-206, June. [Downloadable!] (restricted)
Other versions:
- David Heath & Eckhard Platen, 2004. "Local Volatility Function Models under a Benchmark Approach," Research Paper Series 124, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]

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